Computation of Battle-Lemarie wavelets using an FFT-based algorithm
Jeng‐Fan Leu, Jyh-Cheng Jang, Chyi Hwang · 2002
Battle and Lemarie (1987, 1988) derived independently wavelets by orthonormalizing B-splines. The scaling function /spl phi//sub m/(t) corresponding to Battle-Lemarie's wavelet /spl psi//sub m/(t) is given by /spl phi//sub m/(t)=/spl Sigma//sub k/spl isin/Z//spl alpha//sub m,k/B/sub m/(t-k), where B/sub m/(t) is the mth-order central B-spline. We propose an FFT-based algorithm for computing the expansion coefficients /spl alpha//sub m,k/ and the two-scale relations of the scaling functions and wavelets. The algorithm is very simple and it can be easily implemented. Moreover, the expansion coefficients can be efficiently and accurately obtained via multiple sets of FFT computations.